An exact algorithm for the unidirectional quay crane scheduling problem with vessel stability

This paper addresses the quay crane scheduling problem (QCSP) with vessel stability constraints. Vessel stability is essential to improve quay crane operations in container terminals, but it significantly com- plicates the basic QCSP and the corresponding solutions methods. We describe a novel mathematical formulation for the unidirectional QCSP with vessel stability, and we propose an exact algorithm based on logic-based Benders decomposition to solve the problem efficiently. The problem is decomposed into two subproblems, e.g., a task-assignment master problem without vessel stability constraints, and a time- allocation problem, aimed at determining the operation time of each task under the premise of the vessel stability requirements. The proposed algorithm is tested on benchmark instances derived from the litera- ture, and the effectiveness of the proposed model and solution approach is demonstrated.